Angles Opposite Equal Sides are Equal


 
 
Concept Explanation
 

Angles Opposite Equal Sides are Equal

Theorem: Angles opposite to two equal sides of a triangle are equal.

Given: Delta ABC in which AB = AC

To Prove:  angle C=angle B

Construction:  Draw the bisector AD of angle A which meets BC in D.

Proof: In large Delta sABD;and ;ACD , we have

               AB = AC          [Given]

      angle BAD=angle CAD   [By construction]

            AD = AD            [Common side]

Therefore, by SAS criterion of congruence, we have

        Delta ABDcong Delta ACD

Rightarrow ;;;angle B=angle C        [Corresponding parts of congruent triangles are equal]

Illustration: In Delta ABC, angle A=100^{circ} and AB = AC. FInd angle B and angle C

Solution:  We have,

        AB = AC

Rightarrow ;;angle B=angle C             [because  Angles opp.  to equal sides are equal]

In Delta ABC, we have

      angle A+angle B+angle C=180^{circ}

Rightarrow angle A+angle B+angle B=180^{circ}           [because angle B=angle C]

Rightarrow ;;;100^{circ}+2angle B=180^{circ}

Rightarrow ;;;;;2angle B=80^{circ}

Rightarrow ;;;;;angle B=40^{circ}

Hence,  angle B=angle C=40^{circ}

Sample Questions
(More Questions for each concept available in Login)
Question : 1

In the above figure, angle S=angle T=35^{0}, then which sides will be equal?

Right Option : C
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Explanation
Question : 2

bigtriangleup ABC is an isosceles triangle with AB = AC. Side BA is produced to D such that AB = AD. Then which of the following is true?

Right Option : C
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Explanation
Question : 3

In the following figure, AB = AC and DB = DC. Then which of the following statement is true?

Right Option : B
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Explanation
 
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